PUBLICATIONS
Journal of Geophysical Research: Oceans
RESEARCH ARTICLE
Observed and modeled drifters at a tidal inlet
10.1002/2014JC010541
Key Points:
Observed drifter and current meter
velocities are similar within a tidal
inlet
Observed drifter spreading is larger
than modeled during ebb tide
Observed spreading rates are likely
affected by stratification
Correspondence to:
M. S. Spydell,
[email protected]
Citation:
Spydell, M. S., F. Feddersen,
M. Olabarrieta, J. Chen, R. T. Guza,
B. Raubenheimer, and S. Elgar (2015),
Observed and modeled drifters at a
tidal inlet, J. Geophys. Res. Oceans, 120,
doi:10.1002/2014JC010541.
Received 28 OCT 2014
Accepted 9 JUN 2015
Accepted article online 12 JUN 2015
Matthew S. Spydell1, Falk Feddersen1, Maitane Olabarrieta2, Jialin Chen3, R. T. Guza1,
Britt Raubenheimer4, and Steve Elgar4
1
Integrative Oceanography Division, Scripps Institution of Oceanography, La Jolla, California, USA, 2Department of Civil
and Coastal Engineering, University of Florida, Gainesville, Florida, USA, 3Civil and Environmental Engineering, University
of Delaware, Newark, Delaware, USA, 4Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USA
Abstract Material transport and dispersion near the mouth of a tidal inlet (New River Inlet, NC) are investigated using GPS-tracked drifters and numerical models. For ebb tide releases, velocities are largest (>1 m s21 )
in two approximately 30 m wide channels that bisect the 1–3 m deep ebb shoal. In the channels, drifter and
subsurface current meter velocities are similar, consistent with strong vertical mixing and 2-D hydrodynamics.
Drifters were preferentially entrained in the channelized jets where drifter cluster lateral spreading rates lin
were small (lin 0:5 m2 s21 ). At the seaward edge of the ebb shoal, jet velocities decrease linearly with distance (to 0:2 m s21 , about 1 km from shore), and cluster spreading rates are larger with lout 3 m2 s21 .
Although the models COAWST and NearCom generally reproduce the observed trajectory directions, certain
observed drifter properties are poorly modeled. For example, modeled mean drifter velocities are smaller than
observed, and upon exiting the inlet, observed drifters turn north more than modeled drifters. The model simulations do reproduce qualitatively the spreading rates observed in the inner inlet, the flow deceleration, and
the increase in lout observed in the outer inlet. However, model spreading rates increase only to
lout < 1 m2 s21 . Smaller modeled than observed lout may result from using unstratified models. Noncoincident (in space) observations show evidence of a buoyant plume (Dq51 kg m23 ) in the outer inlet, likely affecting drifter lateral spreading. Generally, drifter-based model performance is good within the inlet channels
where tidal currents are strongest, whereas model-data differences are significant farther offshore.
1. Introduction
Tidal inlets are important transitional regions between estuaries, bays, lagoons, marshes, and the coastal
ocean, and are ubiquitous features of barrier island geography. Tidal inlets are important economically as
navigation routes, and ecologically as conduits through which material flows from estuaries to the ocean.
C 2015. The Authors.
V
Tidal forcing produces strong currents in inlets, with current speeds often >1 m s21 in relatively narrow
channels. During ebb tide, these jets can penetrate deeply (>1 km) onto the shelf. Within shallow inlets, the
flows are generally vertically well mixed (unstratified), due to the large currents, and density gradients are
assumed dynamically unimportant [e.g., Hench and Luettich, 2003]. Tidal inlet hydrodynamics can be
affected by winds [Geyer, 1997] and waves [Bruun, 1978]. For example, near an inlet mouth, modeling studies show that wave-breaking-induced forces can be important in the momentum balance [Bertin et al., 2009;
Malhadas et al., 2009; Olabarrieta et al., 2011; Dodet et al., 2013]. Modeling studies also show that incident
waves affect the inlet ebb tidal jets [Olabarrieta et al., 2014]. Recent observations at New River [Wargula
et al., 2014] and Katama Bay [Orescanin et al., 2014] show that breaking-wave-driven along-inlet (crossshore) radiation-stress gradients can be a substantial component of the along-inlet momentum balance. For
large waves, these wave effects can significantly enhance flood flows and retard ebb flows.
This is an open access article under the
terms of the Creative Commons
Attribution-NonCommercial-NoDerivs
License, which permits use and
distribution in any medium, provided
the original work is properly cited, the
use is non-commercial and no
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made.
Although within the inlet density gradients are not important dynamically, as the flow is vertically well
mixed, stratification can be important offshore. For inlet water that is less dense (warmer or fresher) than
the offshore ocean water, the ebb tide jet rides up and over the denser coastal ocean water as a ‘‘buoyant
plume’’ [Garvine, 1999]. In a buoyant plume, the lighter fluid thins, spreads, and entrains deeper denser
water, with entrainment and spreading linked [Hetland and MacDonald, 2008; McCabe et al., 2008, 2009;
Chen et al., 2009]. There are few Lagrangian studies of plume spreading, and detailed model-data comparisons have not been performed. However, for a single drifter release at the Columbia River Mouth, gross
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features of the observed and modeled drifters in the spreading plume compared well despite differences in
individual trajectories [McCabe et al., 2009].
As inlets connect estuaries to the ocean, estuary-ocean exchange depends in part on tidal inlet hydrodynamics [Liu et al., 2008; Malhadas et al., 2010]. To quantify estuary-ocean exchange and to understand better
the fate of pollution input into estuaries, estuarine residence times have been investigated. Although typically calculated using 2-D unstratified simulations of tidally forced circulation [Bilgili et al., 2005; Yuan et al.,
2007; Arega et al., 2008; Chen et al., 2008; de Brauwere et al., 2011], residence times can depend on stratification [Liu et al., 2008] and wave [Malhadas et al., 2010] processes that often are neglected. In these studies,
unstratified models were typically validated by comparing modeled and observed Eulerian currents within
the estuary. Exchange, material transport, and dispersion are Lagrangian processes, hence models should
be assessed from a Lagrangian perspective. However, Lagrangian model assessments are rare, although,
within an estuary, individual modeled and observed drifter trajectories differed over 6 h [Xu and Xue, 2011].
At inlet mouths, detailed model-data Lagrangian comparisons have not been made.
As part of the RIVET-I experiment, a large Eulerian (current meter) and Lagrangian (drifter) data set was
obtained at the New River Inlet, NC (‘‘NRI’’) to study tidal inlet hydro and morphodynamics. As models are
often used to analyze exchange, but are not well constrained by Lagrangian observations, here Lagrangian
observations are compared with simulated drifter trajectories from two (NearCom and COAWST) numerical
models providing a model-data comparison of tidal inlet flow from a Lagrangian perspective. This is in contrast to the majority of model validation studies which are from an Eulerian perspective [e.g., Kumar et al.,
2015]. However, Eulerian model-data validations for the RIVET-I experiment using these models are in preparation: for NearCom see Chen et al. [2015] and for COAWST see M. Olabarrieta et al. (manuscript in preparation, 2015). As flows within inlets are vertically well mixed, stratification is neglected in both NearCom and
COAWST. The validity of this assumption will be investigated using the observed and modeled drifter data
sets.
The paper is organized as follows. A brief description of the experiment, including the bathymetry, instrumentation, and environmental conditions is provided in section 2. The models are described in section 3.
Observed Lagrangian (drifter) and Eulerian (current meter) velocities are compared in section 4, and
observed drifter velocities and spreading rates are presented in section 5. Observed and modeled Lagrangian statistics are compared in section 6. The differences between the observed and modeled Lagrangian
statistics are discussed in regards to stratification (section 7), and the results are summarized in section 8.
2. New River Inlet Observations
Observations of tidal inlet flows were collected at the New River Inlet, North Carolina (NRI) during May 2012.
This tidal inlet is on a barrier island that faces south east (Figure 1) with the community of Topsail on the
south-west side of the inlet and the Marine Corps station Camp Lejeune on the north-east side of the inlet.
A local coordinate system is chosen where the origin is in the inlet-mouth center, x increases offshore, and
y increases to the northeast (588 from true, Figure 1). The inlet is approximately 1000 m wide at the mouth
(x 5 0 m) and narrows to 500 m wide approximately 500 m upstream of the mouth (x 5 2500 m). On 1–2
May, the inlet bathymetry was surveyed (for 21000 < ðx; yÞ < 1000 m) on cross-shore lines with 50 m
alongshore spacing. Surveyed bathymetry was interpolated to a regular grid (contours in Figure 1) and was
smoothly embedded into an existing digital elevation model (with 10 m resolution) of the New River Inlet
region. The inlet bathymetry shows four distinct features: (1) a large ebb tidal delta off the Topsail (south)
side of the inlet, (2) the early April 2012 dredged ‘‘new’’ navigation channel adjacent to this shoal, (3) the
previously dredged ‘‘old’’ navigation channel closer to Camp Lejeune, and (4) the narrow and deep (up to
11 m) channel that hugs the Topsail side of the inlet. In general, offshore of the inlet mouth (at y 5 0), the
bathymetry is shallow out to x 5 750 m, after which the depth increases quickly offshore. South of the inlet
mouth (for example at y 5 21000 m), the depth increases more uniformly from the shore (Figure 1).
Instruments were deployed within and seaward of the inlet (see legend in Figure 1). Near the mouth of the
inlet, depth-dependent currents were measured with 16 Acoustic Doppler Current Profilers (ADCPs) sampling once a minute, and near bottom currents were measured with 22 Acoustic Doppler Velocimeters
(ADVs) sampling at 1 or 2 Hz. At all current meter locations, bottom pressure and temperature were also
measured. A profiling wirewalker mooring measuring depth and time-dependent temperature and salinity
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was colocated with an ADCP
1000 m offshore of the mouth
of the new channel in 8 m water
depth (yellow in Figure 1). Wave
heights and directions were
obtained from a waverider buoy
deployed by the U.S. Army Corp
of Engineers Field Research
Facility in 12 m water depth
6.1 km offshore of the inlet.
Additionally, a meteorological
station was installed on top of a
piling positioned on the ebb
shoal (at ðx; yÞ5ð2100; 2450Þ
m, blue x in Figure 1).
GPS-tracked drifters [Schmidt
et al., 2003] were deployed
repeatedly within and just seaward of the New River Inlet on 8
days between 1–4 and 14–17
May. Each of the 21 releases typically consisted of 34 drifters.
There were 1–4 releases per day
resulting in 68–328 drifter hours
of observation each day.
Releases are identified by the
Figure 1. Plan view of the New River Inlet bathymetry as a function of cross-shore x and
day and release number, e.g.,
alongshore y coordinates. Depth is colored (scale on the right) and surveyed bathymetry
d1r1 refers to the first release on
is contoured (black curves) at 1 m intervals. Locations of instruments (red symbols, see
legend in the top left), meteorological station (blue ‘‘x,’’ z 5 4.3 m), colocated ADCP and
1 May and d5r2 refers to the
wirewalker (ðx; yÞ5ð970; 0Þ m, yellow), and four prominent bathymetric features are indisecond release on 14 May. Of
cated. The on/offshore velocity of the green colored ADCP (‘‘ADCP0’’) is used to assess the
the 21 total releases, 14 were
tidal phase. Velocities at ADCPs ‘‘A,’’ ‘‘B,’’ and ‘‘C’’ are compared to model velocities in section 3.3.
during ebb tide, 4 were during
flood, and 3 during slack. Here,
six ebb releases are analyzed in detail and for these releases: (1) drifter initial locations were near the inlet
mouth (x 2500 m, Figure 2a), (2) drifters completely exited the inlet, and (3) maximum ebb tidal velocities were similar (Figure 3a). Although the ebb velocities are similar, the 14–17 May ebb releases are not
analyzed in detail because release locations were farther upstream (x < 21000 m) and many drifters did
not exit the inlet. For the six ebb releases examined here, the 34 drifters were deployed within approximately 100 m of each other over 5 min, resulting in a unique initial time and position for each drifter.
The drifters were 0.5 m tall [Schmidt et al., 2003] and rarely encountered the bottom. Drifter tracks were
quality controlled to exclude data contaminated by dragging. For each quality controlled drifter track, colocated drifter position ~
X ðtÞ and velocity ~
u L ðtÞ time series are derived from 1 Hz GPS positions
~
~
X ðtÞ5ðXðtÞ; YðtÞÞ, as ½X ðt1dtÞ1~
X ðtÞ=2 ! ~
X ðtÞ and ½~
X ðt1dtÞ2~
X ðtÞ=dt ! ~
u L ðtÞ. Absolute position errors
are 62 m, but vary slowly in time and result in relatively small errors in drifter relative position and velocity [Schmidt et al., 2003]. Drifter wind slip, estimated as roughly 1% of the wind speed [Schmidt et al., 2003]
is not accounted for. The drifters also measured near-surface water temperature.
During the 21 drifter releases, a range of tide, wind, and wave conditions were encountered (Figure 3). Depthaveraged cross-shore velocity uE near the inlet-center ðx; yÞ5ð2150; 2230Þ m (green in Figure 1, denoted
ADCP0) generally varies between 20.5 m s21 (flood) and 11.0 m s21 (ebb) (Figures 3a and 3b). Thus, on 1
May, the first and second releases (dark shading in Figure 3a) were during ebb tide and the third release was
during flood tide (light shading). The six ebb releases analyzed here, where drifters were released close to the
inlet mouth and exited the inlet, are indicated by dark shading. The remaining 15 releases are indicated by
light shading and are not analyzed in detail. Seven of these releases were also ebb tide releases (e.g., d5r1),
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but had initial drifter locations far
upstream of the inlet mouth and
drifters did not completely exit
the inlet. The remaining eight
releases were during either flood
(e.g., d1r3) or slack tide (e.g.,
d2r2).
Wind speeds during drifter
releases were 1–9 m s21 (Figures
3c and 3d) and were from
approximately 2458 (in experiment coordinates) on d1,2,3,4,6,7;
approximately onshore (08) on d5;
and from 22008 on d8 (Figures
3e and 3f). At the offshore buoy,
significant wave heights were
0.5–1.3 m (Figures 3g and 3h)
with mean directions from
approximately 2158 on d1,5,6,7,8;
from 08 on d3 and d4r3,4; from
108 on d2; and from 408 on
d4r1,2 (Figures 3h and 3i). Peak
wave periods were 5–8 s (not
shown).
3. Models
Observed drifter trajectories are
simulated by two models,
COAWST and NearCom, that simulate currents forced by waves,
winds, and tides. In both models,
wave-current interactions are
included, and the effects of stratiFigure 2. Example trajectories for a typical (a) ebb release (d1r2) and (b) flood release
fication are neglected. Both mod(d1r3). Initial drifter locations are blue dots and fixed instrument locations are red dots.
Water depth is colored (scale at top). Release-averaged wind vectors are dark blue arrows
els use the wave generation and
(lower left) and wave properties (significant wave height and direction) are in white
propagation model SWAN (Simu(upper right). Red dots are current meter locations.
lating WAves in the Nearshore
[Booij et al., 1999]), with frequency
resolution Df 50:025 Hz and directional resolution 68. The circulation models and SWAN are forced with 5 min
wind and atmospheric pressure observations at the meteorological station (blue x in Figure 1), assumed spatially
uniform. Both models are forced on the boundary by tides with tidal constituents provided by the ADCIRC database. Model grids are generated from a high-resolution bathymetric survey near the mouth (from 11 May 2012)
and a larger domain digital elevation model (Figure 1).
3.1. COAWST
The coupled ocean-atmosphere-wave-sediment-transport modeling system (COAWST) [Warner et al., 2010;
Olabarrieta et al., 2011] used here includes SWAN and an ocean model ROMS (Regional Ocean Modeling
System) [Shchepetkin and McWilliams, 2005; Haidvogel et al., 2000, 2008]. ROMS is a three-dimensional, freesurface, terrain-following numerical model that solves finite-difference approximations of the Reynoldsaveraged Navier-Stokes (RANS) equations using the hydrostatic and Boussinesq assumptions [Haidvogel
et al., 2000; Chassignet et al., 2000]. Wave-averaged momentum balance equations [McWilliams et al., 2004;
Uchiyama et al., 2010] are implemented in the COAWST modeling system [Kumar et al., 2012]. A detailed
description of the modeling system can be found in Kumar et al. [2012]. For this experiment,
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Figure 3. Environmental conditions versus time, (left column) 1–5 May 2012 and (right column) 14–18 May 2012: (a and b) depth-averaged cross-shore ADCP velocities uE near the inlet
mouth (green dot in Figure 1), (c and d) wind speed juwind j, (e and f) wind direction hwind , (g and h) incident significant wave height Hs , and (i and j) wave direction hwave in degrees relative to normal incidence. Drifters were released during the 21 shaded intervals with the six ebb releases analyzed in detail indicated by darker shading.
Olabarrieta et al. (manuscript in preparation) provide extensive comparisons of COAWST with waves and
currents measured with the fixed instruments.
SWAN and ROMS models used the same, nested horizontal curvilinear grids. The parent grid, with 60 m
average resolution, spans 50 km in the cross shore from the upper limit of the estuary to 15 km offshore
( 25 m water depth), and at the inlet mouth spans 22 km alongshore. The child grid is centered at the inlet
(ðx; yÞ5ð0; 0Þ m) spanning approximately 7 km in the cross shore and 8 km in the alongshore with 10–15 m
grid resolution. ROMS parent and child grids used five equally spaced sigma vertical layers. SWAN boundary
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conditions were derived from the NOAA database of operational output (WAVEWATCH III version 2.22 hindcast). In ROMS, tidal forcing propagates along the boundary. The coupled ROMS-SWAN hindcast simulations
were run from 1 to 21 May 2012.
3.2. NearCom
New River Inlet hydrodynamics were also modeled [Chen et al., 2015] using NearCom-TVD [Shi et al., 2003],
which couples SWAN [Booij et al., 1999] and a curvilinear quasi-3-D nearshore circulation model SHORECIRC
[Svendsen et al., 2004]. SHORECIRC is a two-dimensional horizontal (2-DH) model that incorporates the mixing effect induced by the vertical variation of wave-induced horizontal circulation [Putrevu and Svendsen,
1999]. For a well-mixed coastal environment with negligible baroclinic gradients, quasi-3-D models are similar to full 3-D circulation models [Haas and Warner, 2009]. In some applications, the computational efficiency
of NearCom relative to depth-resolving models is advantageous.
NearCom model resolution varies and is similar to COAWST resolution with 10 m resolution in the inlet
mouth and about 200 m resolution offshore and in the backbay area. SWAN boundary conditions (significant wave height and peak period) were derived from NOAA buoy 41036 (25 m depth, 46 km offshore), but
due to missing data at this buoy, mean wave direction is from the waverider buoy (12 m depth, 6.1 km offshore). In NearCom, the tidal forcing is constant at any time along the boundary, and thus does not propagate. The NearCom model setup and comparison with fixed instruments are presented in Chen et al. [2015].
3.3. Eulerian Velocity Model-Data Comparison
Comprehensive model-data comparisons of Eulerian velocities for NearCom [Chen et al., 2015] and COAWST
(Olabarrieta et al., manuscript in preparation, 2015) are presented elsewhere. However, prior to a more
detailed Lagrangian drifter model-data comparison, a limited Eulerian velocity model-data comparison, spanning the six analyzed ebb releases on 1–4 May, is performed at three ADCP locations within the inlet, within
the old channel, and at the seaward edge of the ebb shoal (denoted A, B, and C, respectively in Figure 1). At
each ADCP, the observed velocities are rotated into velocity principle axes (which generally coincide with the
local bathymetry contours, Figure 1) with major axis Up and minor axis Um velocities (black curves Figure 4)
that have rotation angles hr 5 158, 228, and 128 counterclockwise from 1x for A, B, and C, respectively.
COAWST and NearCom model velocities are also rotated into the observed principal axis coordinate.
Observed velocity (black curves Figure 4) is largest within the inlet (location A) and smaller farther offshore
(location C). At location A, observed principal-component tidal velocity Up (black curve Figure 4a) is 1 m
s21 at maximum ebb and 20:5 m s21 during maximum flood and is largely semidiurnal. At location B,
observed Up has similar maximum ebb velocity as location A, but smaller (Up 20:25 m s21 ) maximum
flood velocities. Farther offshore at the seaward edge of the ebb shoal (location C), observed Up maximum
ebb ( 0:5 m s21 ) and flood ( 20:1 m s21 ) velocities are weaker than at instruments A and B. Observed
minor axis velocities Um (black curves Figures 4d–4f) are smaller than Up and have little tidal signal. In addition, during the ebb drifter releases (dark gray shading in Figure 4), at all three locations, the observed Um
> 0 indicating 1y flow during ebb tide (recall the rotation angle is small).
At these three locations, modeled and observed velocities show similarities and differences (Figure 4). In
particular, the observed and modeled principal axis velocities Up have similar magnitudes and phases (Figures 4a–4c), except that the COAWST Up magnitude at A is larger than observed, and observed ebb tide Up
is larger than COAWST and NearCom at B (and to a lesser extant at C). At locations A, B, and C, the modeldata root-mean-square Up error is 0.15 (0.19), 0.27 (0.24), and 0.14 (0.20) m s21 , respectively, for COAWST
(NearCom). At location A, NearCom model Up errors are larger because the modeled flood to ebb transition
leads the observations by 1 h (Figure 4a). Although the observed minor axis velocity Um have little tidal
signal, the COAWST and NearCom modeled Um have a tidal component at location A (red and green curves
in Figure 4d), indicating that modeled principal axes are 8 off of the observed principal axis. At location
B in the old channel, modeled and observed Um are similar (Figure 4e). However, at the seaward edge of
the ebb shoal (location C) modeled, Um is less than observed.
3.4. Modeled Drifter Tracks
NearCom provides depth-average Lagrangian velocities ~
u L;m that are the sum of mean Eulerian velocities
~
u E;m and Stokes drift ~
u S;m , i.e., ~
u L;m 5~
u E;m 1~
u S;m . Stokes drift velocities are relatively small in both NearCom
and COAWST. COAWST provides depth-dependent velocities and the mean surface Lagrangian velocities
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Figure 4. Modeled (red and green) and observed (black) depth-averaged velocities for the first 2 days of May at three ADCPs (A, B, and C, see Figure 1). Modeled and observed velocities
are in observed velocity principle axis coordinates (at angles 158, 228, and 128 counterclockwise from 1x for A, B, and C, respectively). (a, c, and e) Principle axis velocities Up are positive
out of the inlet and (b, e, and f) minor axis velocities Um are positive 908 left of positive Up. Gray shading indicates drifter release times with dark shading indicating ebb releases.
are used to advect modeled drifters, however, results are not sensitive to using depth-averaged COAWST
velocities. Modeled drifter trajectories ~
X m are obtained by offline integration of
ðt
~
X m ðt50Þ1 ½~
u L;m ð~
X m ðt0 Þ; t0 Þ1wðt0 Þ dt 0 ;
(1)
X m ðtÞ5~
0
where (1) is discretized with a forward Euler step. Model velocities are spatially linearly interpolated to
model drifter positions, because modeled drifter positions are not at model grid points. Although (1) is only
first-order accurate in time, modeled drifter paths would not differ substantially if a higher-order method
were used as the time step Dt52 s used is small compared to both the time scale over which the currents
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are changing (tidal) and the
advective time scale L=U
1000 s, where L is the length
scale over which velocities
change in the direction of U.
Sufficient to resolve the tidal
flows, modeled velocity fields
~
u L;m are separated by 10 and 5
min for COAWST and NearCom,
respectively, and linearly interpolated in time in the time stepping procedure. For each drifter
track, the modeled initial drifter
positions ~
X m ðt50Þ are equal to
the observed drifter release
location, and the subsequent
trajectory durations are equal.
Figure 5. Drifter-mean Lagrangian ~
U L (thin black arrows) and Eulerian ~
U E (red arrows)
Thus, all 34 observed and modvelocities for d1r1. ADV velocities are red arrows without dots and ADCP velocities are
depth averaged and indicated by red arrows with red dots. The bathymetry is colored
eled drifter tracks are unique,
(scale at right). The wind direction and magnitude are indicated in blue, and the wave
even though modeled drifter
direction and significant wave height are indicated in black (bottom right).
releases have the same number,
initial positions, and durations
as the observed drifters. To represent turbulent processes not resolved by the models, and to better match
the higher-frequency observed Lagrangian velocities, weak horizontal diffusion, equivalent to
j50:1 m2 s21 , is added to each trajectory by including the random Weiner process wðt 0 Þ [e.g., Berloff and
McWilliams, 2002]. The sensitivity of modeled drifter tracks to the value of j was explored, and the results
presented here do not depend on j as long as j 0:1 m2 s21 . Model drifters that would cross a land
boundary are reflected back into the fluid, conserving drifters.
4. Comparison of Observed Lagrangian With Eulerian Velocities
At NRI, the observed drifters often closely passed (within < 50 m) current meters (see Figure 2) providing an
opportunity to directly compare Lagrangian (drifter) with Eulerian (current meter) velocities. For each
release, the drifter-mean Lagrangian velocity ~
U L 5ðUL ; VL Þ at a current meter is defined as the average of all
drifter velocities ~
u L ðtÞ for all drifters that passed within 50 m of a current meter. Thus, multiple drifters that
pass the same current meter can contribute to ~
U L . The results do not change appreciably for radii between
25 and 100 m. The drifter-mean Eulerian velocity ~
U E 5ðUE ; VE Þ is calculated as the time average of the current meter velocities ~
u E ðtÞ over the times that drifters were within 50 m of the current meter. In calculating
the drifter-mean Eulerian velocity time-average, times are weighted by the number of drifters that pass the
current meter. For example, if three drifters passed by a current meter for the times t0 < t < t1 , this time
period is given triple weight in the average. Drifter-mean Lagrangian ~
U L and Eulerian ~
U E velocities are calculated at each current meter that drifters closely passed for all 21 drifter releases.
Before comparing drifter-mean Lagrangian with Eulerian velocities for the entire experiment, a single
release is examined. For the d1r1 release, drifter-mean Lagrangian ~
U L and Eulerian ~
U E velocities compare
well within the inlet (black and red arrows in Figure 5), even at the deepest (h 8 m at
ðx; yÞ ð2800; 2300Þ m) current meter within the inlet channel. Consistent with boundary layer flow, the
surface sampled drifter velocities (j~
U L j) are usually only a little larger than the near-bed (ADV) or depthaveraged (ADCP) current meter velocities (j~
U E j), suggesting the flow within the inlet is mostly vertically uniform but slightly larger at the surface.
U E compare poorly (white circles in Figure 5, h 4 m),
At the outer-edge of the ebb-tidal shoal, ~
U L and ~
~
~
where jU L j is small and jU E j is near zero, suggesting that surface and near-bottom velocities can differ significantly at the outer limit of the inlet mouth. Surface Stokes drift velocities and surface horizontal velocity
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Figure 6. Drifter-mean Lagrangian versus drifter-mean Eulerian velocities: (a) cross-shore UL versus UE, and (b) alongshore VL versus VE.
Dashed lines are linear best fits to the 183 points with slopes of 1.06 for U (R2U 50:92) and 1.05 for V (R2V 50:94). Open circles are values for
the ADVs at the outer-edge of the ebb-tidal shoal (red pluses in Figure 1).
gradients could contribute to this difference between drifter-mean Lagrangian and Eulerian velocities, however, these factors are too small to explain the large difference indicated in Figure 5.
U E are also similar for all 21 releases (183 total velocities)
Consistent with the d1r1 release (Figure 5), ~
U L and ~
in both velocity components U and V (Figure 6). An exception to the usually good agreement is at the
outer-edge of the ebb-tidal shoal (red 1s in Figure 1) where UE (and VE) is near zero, but UL (and VL) is not
always small (open circles in Figures 6a and 6b). Using all data points, the square correlation (R2) between
the drifter-mean Lagrangian and Eulerian velocities is high for both cross-shore (R2U 50:92, Figure 6a) and
alongshore (R2V 50:94, Figure 6b) components and rms errors are 0.17 and 0.13 m s21 for U and V, respectively. The best fit slopes indicate ~
U L 1:05 ~
U E (dashed lines in Figures 6a and 6b), consistent with the d1r1
faster (surface) j~
U L j than (near bed or depth average) j~
U E j. Thus, within the inlet, drifters and current meters
are sampling the same nearly vertically uniform boundary layer flow field that is slightly surface intensified.
For the small waves during the drifter releases, Stokes drift velocities (calculated using linear theory) are
small (Oð0:01Þ m s21 ), and thus do not affect UL.
5. Ebb Lagrangian Observations
Observations of drifter trajectories, velocities, and cluster spreading statistics are discussed for six ebb
releases where drifters transitioned from the inlet to the shelf, similar to previous studies at larger systems
[McCabe et al., 2008; Hetland and MacDonald, 2008].
5.1. Drifter Paths and Velocities
Drifter velocities ~
u L are spatially binned (50 by 50 m bins) by drifter positions ~
X L to derive surface mean
velocity maps for each release. Velocities range between 1.25 m s21 in the channels to near zero offshore.
Flow patterns are generally similar for the six releases (Figure 7), as expected given the similar release locations and tidal phase. Drifters exit the inlet preferentially through either the new or old channels (see Figure
1). After passing through the relatively narrow channels, velocity magnitudes decrease as drifters move into
the deeper coastal-ocean waters offshore of the ebb tidal shoal (as in Hetland and MacDonald [2008]). Offshore of the ebb shoal, the drifters turn leftward and advect in the 1y direction, perhaps due in part to the
1y wind component present on all releases (blue arrows in Figure 7) or to the 1y wave component present
on two releases (green arrows in Figures 7a and 7b).
The d1r1, d2r1, and d4r2 velocity magnitude maps (Figures 7a, 7b, and 7f) are nearly synoptic as inlet tidal
velocities (Figure 3a) did not change significantly over the duration (< 2 h) of the release, similar to maximum ebb at other locations [Hetland and MacDonald, 2008] and consistent with momentum balances at
tidal inlets in which local accelerations (du/dt) are small during maximum ebb [Hench and Luettich, 2003].
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Figure 7. Spatially binned (in 50 by 50 m bins) Lagrangian velocity magnitude (colored blue to red, scale in upper left) over the bathymetry (colored white to brown, scale in upper right)
for the six ebb releases: (a) d1r1 to (f) d4r2. Current meter locations (black dots), wind direction hwind , and magnitude juwind j (blue), wave direction hwave , and significant wave height Hs
(white), are indicated. Black dots are current meter locations.
The d3r1 velocity map (Figure 7d) is also synoptic across the ebb tidal shoal (x < 1000 m) as drifters passed
through this region quickly due to the large velocities (>0.3 m s21 ) in this region.
5.2. Spreading
To prevent falsely assigning dispersion to drifters exiting through different channels, clusters of drifters are
considered separately. Specific drifter clusters exited through either the old channel or the new channel (Figures 2a and 7). For example, d1r1 (Figure 7a) has two obvious clusters, d1r1-new and d1r1-old, corresponding
to new and old channel exits, respectively. For the six ebb releases, there are 1–2 clusters per release and a
total of 11 drifter clusters including 5 that exited the new channel and 6 that exited the old channel.
For each cluster, the cluster center of mass is
~
X ðtÞi;
X c ðtÞ5h~
(2)
where ~
X ðtÞ is the drifter position and averaging, denoted by hi is over all drifters in the cluster. The cluster
velocity is then
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d
~
X c ðtÞ :
U c ðtÞ5 ~
dt
(3)
The cluster cloud size is found
by calculating the drifter position covariance matrix Dij
Dij ðtÞ5hXi ðtÞXj ðtÞi2Xc;i ðtÞXc;j ðtÞ;
(4)
where i and j refer to direction. At
every t, the position covariance
matrix Dij is diagonalized to obtain
the major a(t) and minor b(t) axes,
and the angle a that the principle
axis makes with the 1x axis.
Figure 8. Drifter tracks for the d1r1 release superposed on bathymetry (colors, scale on
right). Green (black) drifter tracks exited the old (new) channel. Standard deviation ellipses, with principle and minor axis lengths a(t) and b(t), respectively, about the cluster center of mass ~
X c ðtÞ are shown every 5 min. The critical point separating inner and outer inlet
regions along a cluster track (magenta dots) is defined in reference to ðx0 ; y0 Þ5ð500; 200Þ
m and (500, 650) m for the old and new channel clusters, respectively (white stars).
Drifter cluster cloud ellipses
centered at ~
X c ðtÞ, for both of
the d1r1 clusters are shown in
Figure 8. The d1r1 old channel
cluster (d1r1-old, green tracks in
Figure 8) shrinks as it enters the
old channel and then grows
rapidly upon entering deeper
water (at ðx; yÞ ð600; 600Þ m).
The d1r1-new cluster cloud
(black tracks in Figure 8) also
grows rapidly upon entering
deeper water (at ðx; yÞ ð750;
200Þ m).
The cluster spreading rate l, defined as
l5
1d
D;
2 dt
(5)
where DðtÞ5aðtÞbðtÞ is related to the drifter ellipse area A, A5pD, is calculated for each cluster and
smoothed in time with a 3 min low-pass filter. For all releases, cluster spreading rates l (Figure 9) indicate
that spreading l > 0 (red colors) occurs when drifters enter deeper water (x > 500 m) in contrast to nearzero l in regions within the inlet. Spreading rates l also indicate that old channel drifter clusters (upper
tracks in each panel) often contract in the old channel (l < 0 in Figures 9a, 9c, 9e and 9f) before expanding
(see Figure 8). For the drifter clusters exiting the new channel, the spreading rate is more variable between
releases. However, large positive spreading rates for new channel exits are found when drifters enter deeper
shelf waters for d1r1, d3r1, and d4r2 (Figures 9a, 9d, and 9f).
The offshore increase in l is quantified by averaging l over distinct inner and outer inlet regions. The
boundary between inner and outer inlet regions (x0, y0) for the new and old channels, ðx0 ; y0 Þ5ð500; 200Þ
and (500, 650) m, respectively (stars in Figure 8), is where the channel width begins to increase and the
channels become less well defined. As clusters do not exactly pass (x0, y0), the cluster location closest to (x0,
y0) is taken as the transition from inner to outer inlet (magenta dots in Figure 8). Averaged over all 11 clusters, the average inner-inlet spreading rate lin 50:5 m2 s21 is smaller than the outer inlet spreading rate
lout 52:8 m2 s21 .
Cluster velocities j~
U c j and spreading rates l vary with downchannel distance l from (x0, y0) (Figure 10). For
d1r1 (Figure 7a), j~
U c j decreases linearly with l until a roughly constant 0:25 m s21 is reached at
x 5 1000 m in both the new and old channels (grey dashed lines in Figures 10a and 10b). For the new channel cluster, j~
U c j is maximum at the release location (Figure 10a), whereas for the old channel, j~
U c j is maximum downstream of the release location (Figure 10b). A linear dependence of j~
U c j on l (constant dj~
U c j=dl)
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Figure 9. The cluster spreading rate l (colored blue to red, scale on upper left) for the six ebb releases on the cluster trajectory ~
X c ðtÞ. Bold magenta dots separate inner and outer
regions. The axis limits in Figure 9d are larger than the other plots. White to brown colors are bathymetry (scale on upper right). Black dots are current meter locations.
is found for all 11 clusters. A linear best fit for the 700 m span downstream of the j~
U c j maximum yields average new channel dj~
U c j=dl524:631024 s21 and old channel dj~
U c j=dl525:131024 s21 decelerations.
The relationship between cluster spreading and cluster velocity as drifters move onto the shelf is similar to
plume spreading where cluster (plume) velocities decrease downstream while cluster (plume) widths
increase downstream [McCabe et al., 2008]. However, the present decelerations dj~
U c j=dl 2531024 s21
24 21
are larger than those reported for the Columbia River Mouth ( 21310
s ) [McCabe et al., 2008].
6. Comparison of Observed and Modeled Drifters: Trajectories, Velocities, and
Spreading
For the 34 drifters of the d1r1 release (similar to other ebb releases, Figure 7), observed and modeled trajectories have similarities and differences (Figure 11). A much larger fraction of observed drifters (black in Figure 11) take the old channel exit path than the modeled (red and green in Figure 11) drifters, which
preferentially exit the new channel (see Figure 1 for orientation). The difference between observed and
modeled paths originates near the release location (star in Figure 11), with observed drifters heading to the
left (toward 1y) approximately 500 m from the release location, a feature not present in the model trajectories. This difference is due to weaker modeled than observed cross-channel velocity (v) in this region during
ebb tide. In this region during the ebb drifter releases (dark gray shading Figure 4b), observed crosschannel flow (Um) is positive (toward Camp Lejuene), whereas modeled cross-channel flow is negative. It is
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Figure 10. The cluster velocity magnitude (black), spreading rate (red), and temperature (green) versus downstream distance l, with l 5 0
separating inner and outer regions, for (a) a new channel cluster exit d1r1-new and for (b) an old channel cluster exit d1r1-old. The decelerating jUc j-l best fit lines are indicated by thick dashed gray lines. Spreading rates and temperatures for l < 0 are thin curves (i.e., lin ) and
for l > 0 are thick curves (i.e., lout ).
not known why the models do not reproduce the observed cross-channel flow in this region. However,
observed and modeled differences in the cross-channel flow in this region may be related to weaker modeled
velocities in the old channel (Figure 4c). Thus, weaker modeled old channel flow may be responsible for fewer
modeled drifters exiting the old channel. The few observed (black) and many COAWST (red) modeled drifters
that exit the new channel take a
sharp left turn upon entering
deeper waters near ðx; yÞ ð750;
200Þ m. In contrast, NearCom
(green) modeled new channel
exiting drifters move straight offshore. Observed, COAWST, and
NearCom drifter path differences
may be due to model boundary
conditions, imperfect bathymetry,
model resolution, and assuming
spatially homogeneous winds.
However, better COAWST than
NearCom drifter paths may indicate that resolving the vertical
structure of the flow at the inlet
mouth may be critical to drifter
exit paths or that including progressive tidal propagation on the
boundaries is important as tidal
forcing is progressive in COAWST
but standing in NearCom. Inlet
Figure 11. All observed (black), COAWST (red), and NearCom (green) drifter tracks for the
flows and their symmetry depend
d1r1 release. Initial drifter locations are near the blue star. Observed wind magnitude and
on whether offshore tides
direction (blue) and significant wave height and direction (white) are indicated. White to
propagate progressively with
brown colors are bathymetry (scale on the right).
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alongshore propagating tides
producing asymmetric flows in
the inlet region [van der Vegt
et al., 2009].
Figure 12. The d2r1-old cluster track ~
X c for: (black) observations, (red) COAWST model,
and (green) NearCom model. Initial cluster track positions are shown by open circles and
the location separating inner and outer inlets is indicated by large magenta dots. Bathymetry is colored (scale on the right).
To test the sensitivity of modeled
drifter paths on the drifter release
location, a numerical experiment
was performed in which modeled
drifters were released close to
(every 10 m within a 50 3 50 m
square), but not at the observed
drifter release locations. For this
experiment, modeled drifter tracks
were not significantly different
than the model tracks reported,
namely, modeled drifters still preferentially exited the new channel
and in general had smaller alongshore displacements than the
observed drifters. Hence, modeled
drifter tracks are not sensitive to
the precise release location as
long as it is close to the observed
release location.
Model drifter cluster velocities (~
U c ðtÞ) and spreading rates (l) are calculated in the same manner as the
observations (see section 5.2). Clusters are based upon drifters exiting either the old or new channels (and
not drifter initial locations), thus the observed, COAWST, and NearCom clusters are determined independently of each other and do not necessarily include the same drifters. Consequently, the number of drifters
in observed and modeled clusters differ in addition to observed and modeled clusters having different initial positions. The observed and modeled d2r1-old drifter cluster is compared in detail as this is the only
case where observed, COAWST, and NearCom modeled clusters all exit the old channel (Figure 12). Moreover, for this case, all three clusters turn left toward 1y near the transition from inner to outer inlet,
although the observed cluster turns more sharply left than modeled clusters (Figure 12).
Comparing the observed with the modeled downstream l dependence of jUc j indicates that the observed d2r1old cluster velocity j~
U c j is consistently larger than modeled and the observed and modeled l dependence differs
(compare black curves Figures 13a–13c). In particular, observed j~
U c j 0:6 m s21 for l < 300 m while COAWST
21
~
and NearCom jU c j 0:6 m s only for l < 2700 m. From the release point (l 5 21400 m), the observed cluster initially accelerates from 0.7 to 1.0 m s21 near l 5 – 550 m, and subsequently decelerates roughly linearly
with l. In contrast, COAWST and NearCom models do not reproduce the observed cluster acceleration for l < 2
550 m, and both models have near-release maximum j~
U c j 0:8 m s21 , and a decreasing j~
U c j trend toward the
outer inlet. These cluster velocities are consistent with the larger observed than modeled ADCP ebb velocities in
the old channel (Figure 4c, the ADCP location corresponds to l 2500 m). The observed slope dj~
U c j=dl in the
linear decelerating region is 50% larger than modeled (gray dashed lines in Figure 13).
Some features of the observed cluster spreading rate l are modeled well, and others are not. For the d1r1
release, upon exiting the inlet (near ðx; yÞ ð800; 200Þ m in Figure 11) both COAWST and NearCom modeled
drifter trajectories spread much less than observed. This is evident also in the d2r1-old spreading rate dependence on downstream distance l (Figure 13). Near the release location (l < 2700 m), observed, COAWST, and
NearCom l are relatively small (Figure 13, red curves). Unlike the model clusters, observed clusters are
squeezed into the old channel (l 2300 m) resulting in large negative spreading rates (l 25 m2 s21 ). Also,
the observed clusters expand (l > 0) farther downstream, whereas the modeled spreading rates are near zero.
The observed and modeled features of all 11 clusters (Figure 14) are consistent with the d1r1 release
(Figure 11) and d2r1-old clusters (Figure 13). Observed clusters are more likely to exit the old channel (6
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Figure 13. The d2r1-old cluster velocity magnitude j~
U c j (black) and spreading rate l (red) versus downstream distance l for: (a) observations, (b) COAWST, and (c) NearCom. The point separating the inner and outer inlet is l 5 0. The decelerating jUc j-l best fit lines are indicated by thick dashed gray lines. Spreading rates for l < 0 are thin red curves (i.e., lin ) and for l > 0 are thick red curves (i.e., lout ).
of 11 clusters) relative to the COAWST (2 of 11) and NearCom (3 of 11) clusters. Observed cluster exit
paths are more varied and spread across the inlet than modeled clusters (Figure 14). After exiting,
observed and COAWST clusters turn left (toward 1 y) more strongly than NearCom clusters. Consistent
with the shorter modeled than observed cluster tracks (Figures 13 and 14), COAWST and NearCom cluster velocities are 87% and 66%, respectively, of the observations when averaged along track and over all
11 clusters. Shorter cluster tracks and smaller cluster velocities reflect the weaker modeled than
observed Eulerian velocities in the old channel and at the seaward edge of the ebb shoal (locations B
and C in Figures 4c and 4e). Differences between observed and modeled cluster trajectories are not
improved significantly by including drifter windage effects [Schmidt et al., 2003] equal to 1% of the wind
speed in the models.
Overall, observed and modeled spreading rates are smaller in the inner inlet than in the outer inlet (fewer warm
colors shoreward of magenta dots in Figure 14, especially in the more populated new channel). The averaged
inner-inlet spreading rates lin for observed and model (COAWST and NearCom) clusters are small
lin 0:5 m2 s21 . In contrast, the outer-inlet observed average lout 52:8 m2 s21 is much larger than modeled
lout 0:7 m2 s21 (Figure 14). Due to different observed and modeled trajectory lengths, observed and modeled
mean outer inlet spreading rates are calculated over different regions. However, an experiment was performed in
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which modeled drifters were
allowed to propagate farther onto
the shelf by advecting modeled
drifters for 2 h longer than the
observed. For this experiment, the
results are not different than those
reported and modeled outer inlet
spreading rates are still small relative to the observed.
7. Discussion: Spreading
and Stratification
The observed and modeled cluster
spreading rates l are different in
the outer inlet and deeper coastal
ocean (Figure 14). The causes of this
difference are investigated by examining the relationship between l,
~
U c , and water depth h. For 2-Dhorizontal flow (i.e., shallow water
equations), an initial material volume of incompressible fluid is conserved, but laterally expands or
contracts as the water depth varies
[e.g., Vallis, 2006]. A cylindrical material volume V0 5Ah with area A5pD
and depth h, whose material derivative dV0 =dt50, requires ðdA=dtÞh1
Aðdh=dtÞ50. Substituting l5ð1=
2pÞðdA=dtÞ; AðtÞ5V0 =hðtÞ,
and
dh=dt5~
U c ðtÞ rh, into this expression yields,
l52
V0 ~
ðU c rhÞh22 :
2p
(6)
Thus, a negative l is expected
for a cluster entering deeper
water (positive ð~
U c rhÞ). For all
11 ebb clusters, and for the
outer-inlet spreading rates, the
modeled binned-mean lout and
ð~
U c rhÞh22 are linearly related
with
the
negative
slope
expected for a 2-D-horizontal
Figure 14. Cluster spreading rates l colored (scale on right) on the cluster track ~
X c for (a)
flow (red and green in Figure
observations, (b) COAWST, and (c) NearCom. All 11 clusters are shown with only the first
2 h of d3r1 included. Magenta dots separate inner and outer spreading regions. Bathyme15). Thus, model drifter spreadtry is colored (scale at the top).
ing rates are due to the 2-D
hydrodynamics of the models. In contrast, the slope between observed binned-mean lout and ð~
U c rhÞ
h22 is positive (black in Figure 15), which is inconsistent with 2-D flow hydrodynamics. These observed
and modeled differences are not likely due to model bathymetry resolution or ocean boundary conditions because modeled and observed hydrodynamics are different.
Modeled and observed outer inlet spreading are fundamentally different, likely due to the evolution of the
buoyant plume carrying the drifters [Liu et al., 2008]. Although currents in the inlet channels and on the ebb
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shoals are approximately vertically uniform owing to strong
currents and the relatively shallow depths (Figure 6), stratification offshore of the inlet mouth
was observed during the experiment. In particular, after 16 May
and farther offshore, a slightly
warm and fresh plume, with
both old and new channel contributions, was observed more
than 2 km offshore using an AUV
[Rogowski et al., 2014]. Additionally, vertical profiles of salinity
and temperature on 1 May (Figure 16) in 8 m water depth offshore of the new channel (near
ðx; yÞ ð970; 0Þ m, yellow in Figure 1) indicate that stratification
was present during ebb drifter
Figure 15. Observed (black), COAWST (red), and NearCom (green) binned mean outer
releases, although the inletU c rhÞh22 . Solid lines are best fits to the binned
inlet spreading rates (lout ) versus ð~
ocean density difference is small
means.
(Dq51 kg m23 , Figure 16c). The
1 May vertical profiles show a
thin, fresh (S 5 35.3 psu), warm (T521:4 C) layer of inlet water above salty and colder (S 5 35.8 psu and
T520 C) ocean water (see white dashed curves Figures 16a and 16b). Solar heating slightly warms, and weak
freshwater inflow slightly freshens, the shallow New River Inlet estuary water.
For buoyant plumes, as the surface water slows, spreads, and thins, it also entrains deeper water cooling
the upper layer [e.g., Yuan and Horner-Devine, 2013]. For the ebb-tide Columbia River plume, the entrainment of saltier water into the fresher plume water was observed using CTD equipped drifters [McCabe
et al., 2008]. For the d1r1 release, cluster temperatures decreased as drifter clusters exited the oldchannel, decelerated, and spread (Figure 10). Within the inner-inlet (l < 0 m), the cluster temperature initially increases, likely due to solar heating, reaching a maximum near the inner-to-outer inlet boundary
(see green curves in Figure 10). For l > 0, the drifter cluster decelerates rapidly (gray dashed in Figure 10),
and the cluster spreading rate l increases (red in Figure 10), and the cluster temperature concurrently
drops by DT50:25 C (green in Figure 10b). This is qualitatively consistent with a two-layer buoyant
plume and deeper-water entrainment [Yuan and Horner-Devine, 2013]. Decreasing drifter cluster temperature for l > 0 was observed for 8 of the 11 clusters, further suggesting that the observed non-2-D drifter
spreading (Figure 15) is likely due to buoyant plume effects.
Entrainment rates can be estimated from cluster velocity magnitude j~
U c j and temperature Tc using the
same arguments from which entrainment rates for the Columbia River plume were estimated using drifter
velocities and salinities [McCabe et al., 2008]. With modification for temperature entrainment, the vertical
entrainment velocity for a steady plume is
wE 5
hpl j~
U c j dTc
;
DT dl
(7)
where hpl is the plume thickness and DT is the temperature difference between plume and shelf water.
Although the plume is not steady and precise values of these quantities are not available, reasonable estimates can be made. Using the depth that spreading begins for the plume thickness, hpl 2 m (Figure
16b), j~
U c j 0:5 m s21 (Figure 10b), DT 1 C (from Figure 16b), and dT=dl 0:25=1000 C m21 (from Figure 10b), results in a cluster entrainment rate we 2:531024 m s21 , smaller than, but the same order of
magnitude estimated for the Columbia River plume [McCabe et al., 2008]. Thus, entrainment rates for
weakly stratified systems such as NRI may be comparable to those at larger systems such as the Columbia
River.
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Figure 16. (a) Salinity, (b) temperature, and (c) density (r) versus height above the bed z and time from the wirewalker at ðx; yÞ5ð1000; 0Þ
m in roughly 8 m water depth (yellow marker in Figure 1). The white dashed curve represents the water mass boundary of new warm and
fresh inlet water. The horizontal black dash-dot line at the bottom of each plot represents the duration of ebb tide, i.e., u > 0. The solid
black horizontal lines indicate the duration of the d1r1 and d1r2 releases. Magenta dots indicate the approximate time that clusters
reached the outer inlet. Color scales are on the right.
8. Summary and Conclusions
Transport and spreading near the mouth of a narrow, shallow, weakly stratified tidal inlet (New River Inlet,
NC) are investigated using GPS-tracked drifters and numerical models. For six ebb tide drifter releases,
velocities are largest (>1 m s21 ) in two deep, 30 m wide navigation channels that bisect the 1–3 m deep
ebb shoal. In the channels, surface drifter and subsurface current meter velocities are similar (Figure 6), consistent with strong vertical mixing and the essentially 2-D model hydrodynamics. Drifters were preferentially
entrained and retained in these channelized jets, and lateral spreading of drifter clusters within a jet was relatively weak (Figures 8 and 9). Upon exiting the inlet mouth at the seaward edge of the ebb shoal, jet velocities decrease linearly with downstream distance (to <0.2 m s21 , about 1 km from shore), a deceleration
rate 5 times larger than reported for the Columbia River Mouth [McCabe et al., 2008]. Average spreading
rates increase from lin 0:5 m2 s21 to lout 3 m2 s21 (Figures 10 and 13).
The numerical models COAWST and NearCom do not reproduce the observations quantitatively. For example, observed drifter velocities were larger than modeled (Figure 13), and modeled and observed paths differed in two ways: (1) few modeled (both COAWST and NearCom) drifters exited the old channel, and (2)
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modeled (especially NearCom) drifters do not turn left (toward 1y) as sharply as observed upon exiting the
inlet (Figure 11). Observed and modeled Lagrangian velocity differences are consistent with larger observed
Eulerian velocities in the old channel (Figure 4c), and more observed drifters exit the old channel due to
weaker modeled than observed cross-channel flow in the inlet mouth (Figure 4b). These differences may be
due to model tidal boundary conditions, imperfect bathymetry, model resolution, and the assumption of
spatially homogeneous winds. Better COAWST than NearCom drifter paths upon exiting the inlet may be
due to tidal boundary conditions, suggesting that including progressive tides on the model lateral boundary (as done in COAWST, but not in NearCom) is important.
The model simulations do reproduce qualitatively the relatively small spreading l in the inner inlet, and the
roughly linear jet flow deceleration. However, model spreading in the outer inlet (lout 0:7 m2 s21 ) is
much less than observed (lout 2:8 m2 s21 ), and may be due to neglecting stratification in the models.
AUV observations [Rogowski et al., 2014] and the profiling wirewalker (Figure 16), show that slightly less
dense inlet water often forms a buoyant plume above slightly cooler and saltier ocean water
(Dq51 kg m23 ). Consistent with buoyant plume dynamics, observed drifter temperatures decrease as they
spread (Figure 10) indicating the entrainment of deeper water into the surface.
Although stratification effects are understood to be important for systems with large density differences,
such as the Columbia River plume with Dq 13 kg m23 [McCabe et al., 2008], the results presented here
suggest that buoyancy effects should be considered in the transition from the outer inlet to the coastal
ocean even for weakly stratified systems. Thus, despite good Eulerian velocity model-data comparison at
many locations within the inlet and the coastal ocean using unstratified models such as NearCom and
COAWST [Chen et al., 2015; Olabarrieta et al., manuscript in preparation, 2015], simulating Lagrangian transport and fate through a tidal inlet onto the coastal ocean likely requires using stratified models.
Acknowledgments
Supported by NSF, ONR, and ASD
(R1E). Staff and students from the
Integrative Oceanography Division
(B. Woodward, B. Boyd, K. Smith,
D. Darnell, K. Hally-Rosendahl,
R. Grenzeback, and A. Doria) and WHOI
(L. Gorrell, D. Forsman, S. Kilgallin,
C. Rivera-Erick, R. Yopak, S. Zippel,
D. Clark, A. Wargula, M. Moulton, and
M. Orescanin) were instrumental in the
data collection. Support to J. L. Chen is
provided by ONR (N00014-13-1-0120)
to the University of Delaware. Data
used in this article can be obtained
from Matthew Spydell
([email protected]) or Falk
Feddersen ([email protected]) in
accordance with AGU data policies. We
thank two anonymous reviewers for
helping to improve the manuscript.
Also, N. Kumar and S. H. Suanda are
thanked as they provided helpful
feedback.
SPYDELL ET AL.
References
Arega, F., S. Armstrong, and A. W. Badr (2008), Modeling of residence time in the East Scott Creek Estuary, South Carolina, USA, J. Hydroenviron. Res., 2, 99–108, doi:10.1016/j.jher.2008.07.003.
Berloff, P., and J. McWilliams (2002), Material transport in oceanic gyres. Part II: Hierarchy of stochastic models, J. Phys. Oceanogr., 32(3),
797–830.
Bertin, X., A. B. Fortunato, and A. Oliveira (2009), A modeling-based analysis of processes driving wave-dominated inlets, Cont. Shelf Res.,
29(5–6), 819–834, doi:10.1016/j.csr.2008.12.019.
Bilgili, A., J. A. Proehl, D. R. Lynch, K. W. Smith, and M. R. Swift (2005), Estuary/ocean exchange and tidal mixing in a Gulf of Maine Estuary:
A Lagrangian modelling study, Estuarine Coastal Shelf Sci., 65, 607–624, doi:10.1016/j.ecss.2005.06.027.
Booij, N., R. C. Ris, and L. H. Holthuijsen (1999), A third-generation wave model for coastal regions: 1. Model description and validation, J.
Geophys. Res., 104(C4), 7647–7666, doi:10.1029/98JC02622.
Bruun, P. (1978), Stability of Tidal Inlets: Theory and Engineering, 510 pp., Elsevier Sci., Amsterdam.
Chassignet, E. P., H. G. Arango, D. Dietrich, T. Ezer, M. Ghil, D. B. Haidvogel, C. C. Ma, A. Mehra, A. M. Paiva, and Z. Sirkes (2000), DAMEE-NAB:
The base experiments, Dyn. Atmos. Oceans, 32, 155–183, doi:10.1016/S0377-0265(00)00046-4.
Chen, C., J. Qi, C. Li, R. C. Beardsley, H. Lin, R. Walker, and K. Gates (2008), Complexity of the flooding/drying process in an estuarine tidalcreek salt-marsh system: An application of FVCOM, J. Geophys. Res., 113, C07052, doi:10.1029/2007JC004328.
Chen, F., D. G. MacDonald, and R. D. Hetland (2009), Lateral spreading of a near-field river plume: Observations and numerical simulations,
J. Geophys. Res., 114, C07013, doi:10.1029/2008JC004893.
Chen, J. L., F. Hsu, T. J. Shi, B. Raubenheimer, and S. Elgar (2015), Hydrodynamic and sediment transport modeling of New River Inlet (NC)
under the interaction of tides and waves, J. Geophys. Res. Oceans, 120, doi:10.1002/2014JC010425.
de Brauwere, A., B. de Brye, S. Blaise, and E. Deleersnijder (2011), Residence time, exposure time and connectivity in the Scheldt Estuary, J.
Mar. Syst., 84, 85–95, doi:10.1016/j.jmarsys.2010.10.001.
Dodet, G., X. Bertin, N. Bruneau, A. B. Fortunato, A. Nahon, and A. Roland (2013), Wave-current interactions in a wave-dominated tidal inlet,
J. Geophys. Res. Oceans, 118, 1587–1605, doi:10.1002/jgrc.20146.
Garvine, R. W. (1999), Penetration of buoyant coastal discharge onto the continental shelf: A numerical model experiment, J. Phys. Oceanogr., 29, 1892–1909, doi:10.1175/1520-0485(1999)029<1892:POBCDO >2.0.CO;2.
Geyer, W. R. (1997), Influence of wind on dynamics and flushing of shallow estuaries, Estuarine Coastal Shelf Sci., 44, 713–722, doi:10.1006/
ecss.1996.0140.
Haas, K. A., and J. C. Warner (2009), Comparing a quasi-3D to a full 3D nearshore circulation model: SHORECIRC and ROMS, Ocean Modell.,
26, 91–103, doi:10.1016/j.ocemod.2008.09.003.
Haidvogel, D. B., H. G. Arango, K. Hedstrom, A. Beckmann, P. Malanotte-Rizzoli, and A. F. Shchepetkin (2000), Model evaluation experiments
in the North Atlantic Basin: Simulations in nonlinear terrain-following coordinates, Dyn. Atmos. Oceans, 32, 239–281, doi:10.1016/S03770265(00)00049-X.
Haidvogel, D. B., et al. (2008), Regional ocean forecasting in terrain-following coordinates: Model formulation and skill assessment, J. Comput. Phys., 227(7), 3595–3624, doi:10.1016/j.jcp.2007.06.016.
Hench, J. L., and R. A. Luettich (2003), Transient tidal circulation and momentum balances at a shallow inlet, J. Phys. Oceanogr., 33,
913–932, doi:10.1175/1520-0485(2003)33<913:TTCAMB>2.0.CO;2.
Hetland, R. D., and D. G. MacDonald (2008), Spreading in the near-field Merrimack River plume, Ocean Modell., 21, 12–21, doi:10.1016/
j.ocemod.2007.11.001.
DRIFTERS AT THE NEW RIVER INLET
19
Journal of Geophysical Research: Oceans
10.1002/2014JC010541
Kumar, N., G. Voulgaris, J. Warner, and M. Olabarrieta (2012), Implementation of the vortex force formalism in the coupled oceanatmosphere-wave-sediment transport (COAWST) modeling system for inner shelf and surf zone applications, Ocean Modell., 47, 65–95,
doi:10.1016/j.ocemod.2012.01.003.
Kumar, N., F. Feddersen, Y. Uchiyama, J. McWilliams, and W. O’Reilly (2015), Mid-shelf to surf zone coupled ROMS-SWAN model-data comparison of waves, currents, and temperature: Diagnosis of subtidal forcings and response, J. Phys. Oceanogr., 45, 1464–1490, doi:
10.1175/JPO-D-14–0151.1.
Liu, W., W. Chen, J. Kuo, and C. Wu (2008), Numerical determination of residence time and age in a partially mixed estuary using threedimensional hydrodynamic model, Cont. Shelf Res., 28, 1068–1088, doi:10.1016/j.csr.2008.02.006.
Malhadas, M. S., P. C. Leit~ao, A. Silva, and R. Neves (2009), Effect of coastal waves on sea level in Obidos
Lagoon, Portugal, Cont. Shelf Res.,
29(9), 1240–1250, doi:10.1016/j.csr.2009.02.007.
Malhadas, M. S., R. J. Neves, P. C. Leit~ao, and A. Silva (2010), Influence of tide and waves on water renewal in Obidos
Lagoon, Portugal,
Ocean Dyn., 60, 41–55, doi:10.1007/s10236-009-0240-3.
McCabe, R. M., B. M. Hickey, and P. MacCready (2008), Observational estimates of entrainment and vertical salt flux in the interior of a
spreading river plume, J. Geophys. Res., 113, C08027, doi:10.1029/2007JC004361.
McCabe, R. M., P. MacCready, and B. M. Hickey (2009), Ebb-tide dynamics and spreading of a large river plume*, J. Phys. Oceanogr., 39,
2839–2856, doi:10.1175/2009JPO4061.1.
McWilliams, J. C., J. M. Restrepo, and E. M. Lane (2004), An asymptotic theory for interaction of waves and currents in coastal waters, J. Fluid
Mech., 511, 135–178, doi:10.1017/S0022112004009358.
Olabarrieta, M., J. C. Warner, and N. Kumar (2011), Wave-current interaction in Willapa Bay, J. Geophys. Res., 116, C12014, doi:10.1029/
2011JC007387.
Olabarrieta, M., R. Geyer, and N. Kumar (2014), The role of morphology and wave-current interaction at tidal inlets: An idealized modeling
analysis, J. Geophys. Res. Oceans, 119, 8818–8837, doi:10.1002/2014JC010191.
Orescanin, M., B. Raubenheimer, and S. Elgar (2014), Observations of wave effects on inlet circulation, Cont. Shelf Res., 82, 37–42, doi:
10.1016/j.csr.2014.04.010.
Putrevu, U., and I. A. Svendsen (1999), Three-dimensional dispersion of momentum in wave induced nearshore currents, Eur. J. Mech. B, 18,
409–427.
Rogowski, P., E. Terrill, and J. L. Chen (2014), Observations of the frontal region of a buoyant river plume using an autonomous underwater
vehicle, J. Geophys. Res. Oceans, 119, 7549–7567, doi:10.1002/2014JC010392.
Schmidt, W. E., B. T. Woodward, K. S. Millikan, R. T. Guza, B. Raubenheimer, and S. Elgar (2003), A GPS-Tracked surf zone drifter, J. Atmos.
Oceanic Technol., 20(7), 1069–1075.
Shchepetkin, A. F., and J. C. McWilliams (2005), The regional oceanic modeling system (ROMS): A split-explicit, free-surface, topographyfollowing-coordinate oceanic model, Ocean Modell., 9(4), 347–404, doi:10.1016/j.ocemod.2004.08.002.
Shi, F., I. A. Svendsen, J. T. Kirby, and J. M. Smith (2003), A curvilinear version of a Quasi-3D nearshore circulation model, Coastal Eng., 49,
99–124, doi:10.1016/S0378-3839(03)00049-8.
Svendsen, I. A., K. Haas, and Q. Zhao (2004), Quasi-3D Nearshore Circulation Model SHORECIRC: Version 2.0, 64 pp., Univ. of Del., Newark.
Uchiyama, Y., J. C. McWilliams, and A. F. Shchepetkin (2010), Wave-current interaction in an oceanic circulation model with a vortex force
formalism: Application to the surf zone, Ocean Modell., 34, 16–35, doi:10.1016/j.ocemod.2010.04.002.
Vallis, G. K. (2006), Atmospheric and Oceanic Fluid Dynamics, 745 pp., Cambridge Univ. Press, Cambridge, U. K.
van der Vegt, M., H. M. Schuttelaars, and H. E. de Swart (2009), The influence of tidal currents on the asymmetry of tide-dominated ebbtidal delta, Cont. Shelf Res., 29, 159–174, doi:10.1016/j.csr.2008.01.018.
Wargula, A., B. Raubenheimer, and S. Elgar (2014), Wave-driven along-channel subtidal flows in a well-mixed ocean inlet, J. Geophys. Res.
Oceans, 119, 2987–3001, doi:10.1002/2014JC009839.
Warner, J. C., B. Armstrong, R. He, and J. B. Zambon (2010), Development of a Coupled Ocean-Atmosphere-Wave-Sediment Transport
(COAWST) modeling system, Ocean Modell., 35, 230–244, doi:10.1016/j.ocemod.2010.07.010.
Xu, D., and H. Xue (2011), A numerical study of horizontal dispersion in a macro tidal basin, Ocean Dyn., 61, 623–637, doi:10.1007/s10236010-0371-6.
Yuan, D., B. Lin, and R. A. Falconer (2007), A modelling study of residence time in a macro-tidal estuary, Estuarine Coastal Shelf Sci., 71, 401–
411, doi:10.1016/j.ecss.2006.08.023.
Yuan, Y., and A. R. Horner-Devine (2013), Laboratory investigation of the impact of lateral spreading on bouyancy flux in a river plume, J.
Phys. Oceanogr., 43, 2588–2610, doi:10.1175/JPO-D-12-0117.1.
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